{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "colab_type": "text",
    "id": "view-in-github"
   },
   "source": [
    "<a href=\"https://colab.research.google.com/github/jermwatt/machine_learning_refined/blob/main/notes/4_Second_order_methods/A_9_Quasi.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k0ZyznxqKpNZ"
   },
   "source": [
    "## Appendix A. Advanced First- and Second-Order Optimization Methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook contains interactive content from an early draft of the university textbook <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main\">\n",
    "Machine Learning Refined (2nd edition) </a>.\n",
    "\n",
    "The final draft significantly expands on this content and is available for <a href=\"https://github.com/neonwatty/machine-learning-refined/tree/main/chapter_pdfs\"> download as a PDF here</a>."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k9PKTF3qKpNc"
   },
   "source": [
    "# A.9 Quasi-Newton methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "dXjSo9TMKpNc"
   },
   "source": [
    "While Newton's method is a powerful technique that exhibits rapid convergence for a (especially) convex function $g\\left(\\mathbf{w}\\right)$, it is naturally constrained by $N$ the dimension of the input $\\mathbf{w}$.  In particular it is the quadratic generating Hessian $\\nabla^2g\\left(\\mathbf{w}\\right)$, an $N\\times N$ matrix that limits Newton's method's use to cases where $N$ is (roughly speaking) in the thousands, since it is difficult to even store such a matrix when $N$ is larger (let alone compute with it).  In this Section we give discuss a set of variations on Newton's method that are designed to ameliorate this issue, collectively referred to as *quasi-Newton's methods*.  The main thrust of any such method is - in the Newton-like step - to replace the Hessian with a close approximation that does not suffer from this scaling problem.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/"
    },
    "id": "KUYf2U91KpNc",
    "outputId": "96905e5e-1f50-4f99-8ba7-e41558121506"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: github-clone in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (1.2.0)\n",
      "Requirement already satisfied: requests>=2.20.0 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (2.32.3)\n",
      "Requirement already satisfied: docopt>=0.6.2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from github-clone) (0.6.2)\n",
      "Requirement already satisfied: charset-normalizer<4,>=2 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.4.0)\n",
      "Requirement already satisfied: idna<4,>=2.5 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (3.10)\n",
      "Requirement already satisfied: urllib3<3,>=1.21.1 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2.2.3)\n",
      "Requirement already satisfied: certifi>=2017.4.17 in /Users/jeremywatt/Desktop/machine-learning-refined/venv/lib/python3.10/site-packages (from requests>=2.20.0->github-clone) (2024.12.14)\n",
      "\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m A new release of pip is available: \u001b[0m\u001b[31;49m24.2\u001b[0m\u001b[39;49m -> \u001b[0m\u001b[32;49m24.3.1\u001b[0m\n",
      "\u001b[1m[\u001b[0m\u001b[34;49mnotice\u001b[0m\u001b[1;39;49m]\u001b[0m\u001b[39;49m To update, run: \u001b[0m\u001b[32;49mpip install --upgrade pip\u001b[0m\n",
      "chapter_4_library already cloned!\n",
      "chapter_4_videos already cloned!\n"
     ]
    }
   ],
   "source": [
    "# install github clone - allows for easy cloning of subdirectories\n",
    "!pip install github-clone\n",
    "from pathlib import Path \n",
    "\n",
    "# clone library subdirectory\n",
    "if not Path('chapter_4_library').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/4_Second_order_methods/chapter_4_library\n",
    "else:\n",
    "    print('chapter_4_library already cloned!')\n",
    "\n",
    "# clone videos\n",
    "if not Path('chapter_4_videos').is_dir():\n",
    "    !ghclone https://github.com/neonwatty/machine-learning-refined-notes-assets/tree/main/notes/4_Second_order_methods/chapter_4_videos\n",
    "else:\n",
    "    print('chapter_4_videos already cloned!')\n",
    "\n",
    "# append path for local library, data, and image import\n",
    "import sys\n",
    "sys.path.append('./chapter_4_library')\n",
    "sys.path.append('./chapter_4_videos') \n",
    "\n",
    "# import section helper\n",
    "import section_4_7_helpers\n",
    "\n",
    "# video paths\n",
    "video_path_1 = 'chapter_4_videos/animation_11.mp4'\n",
    "video_path_2 = 'chapter_4_videos/animation_12.mp4'\n",
    "video_path_3 = 'chapter_4_videos/animation_13.mp4'\n",
    "\n",
    "# standard imports\n",
    "import matplotlib.pyplot as plt\n",
    "from IPython.display import Image, HTML\n",
    "from base64 import b64encode\n",
    "\n",
    "def show_video(video_path, width = 1000):\n",
    "    video_file = open(video_path, \"r+b\").read()\n",
    "    video_url = f\"data:video/mp4;base64,{b64encode(video_file).decode()}\"\n",
    "    return HTML(f\"\"\"<video width={width} controls><source src=\"{video_url}\"></video>\"\"\")\n",
    "\n",
    "# import autograd-wrapped numpy\n",
    "import autograd.numpy as np\n",
    "\n",
    "# this is needed to compensate for matplotlib notebook's tendancy to blow up images when plotted inline\n",
    "%matplotlib inline\n",
    "from matplotlib import rcParams\n",
    "rcParams['figure.autolayout'] = True\n",
    "\n",
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "h6wL4_ojKpNe"
   },
   "source": [
    "## Newton's method from the perspective of the gradient function"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "N-OuOcXUKpNe"
   },
   "source": [
    "We have just seen how Newton's method works to find stationary points of a cost function, points where the gradient of the cost function is zero, effectively minimizing the function.  However the classic application of Newton's method is actually towards finding the *zeros* of (polynomial) functions - that is where a function crosses the input plane.  At first glance it may not seem like the Newton's method - at least the way we have viewed it thus far - is applicable to such problems.  That is until we think about what Newton's method is doing in the space where the *gradient of our cost function* lives.  If Newton's method does indeed take steps towards finding the stationary point of a cost function then then we can we can indeed view these steps evaluated not on the cost function, but on the derivative (or gradient more generally) itself.  Any sequence of steps moving towards a stationary point of the cost function itself is naturally - when evaluated by the gradient - a sequence of steps moving towards a zero of the gradient function."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "TcGdYnfxKpNe"
   },
   "source": [
    "Because we will be frequently be manipulating first and second derivatives here, in this Section we will make use of the common (more compact) 'prime' notation to denote the first and second derivative of a single input function $g(w)$\n",
    "\n",
    "\\begin{equation}\n",
    "g^{\\prime}(w) = \\frac{\\mathrm{d}}{\\mathrm{d}w}g\\left(w\\right) \\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,g^{\\prime\\prime}(w) = \\frac{\\mathrm{d}^2}{\\mathrm{d}w^2}g\\left(w\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "zV7iKY2ZKpNe"
   },
   "source": [
    "Now, remember when $N = 1$ the $k^{th}$ that the Newton's step follows directly from the second order Taylor series approximation centered at a point ${w}^{k-1}$ which (in our 'prime' derivative notation) is\n",
    "\n",
    "\\begin{equation}\n",
    "h\\left(w\\right)=g\\left(w^{k-1}\\right)+g^{\\prime}\\left(w^{k-1}\\right)\\left(w-w^{k-1}\\right)+ g^{\\prime\\prime}\\left(w^{k-1}\\right)\\left(w-w^{k-1}\\right)^{2} \n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Nqm9Hoz1KpNf"
   },
   "source": [
    "We want to determine a stationary point of this quadratic (a global minimum of the quadratic if it is convex) by setting the derivative of this quadratic approximation to zero and solving.  This gives our Newton step \n",
    "\n",
    "\\begin{equation}\n",
    "w^k = w^{k-1} - \\frac{g^{\\prime}(w^{k-1})}{g^{\\prime\\prime}(w^{k-1})}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "EtQnujB4KpNf"
   },
   "source": [
    "By following this sequence of steps we are - when beginning in a convex region of a function -  led to a stationary point which is also a local minimum of $g$.  Now, since any stationary point of $g$ is satisfies $g^{\\prime}(w) = 0$, we can think of this simultaneously as a procedure for finding a *zero of our derivative function*.  Indeed we can easily derive this same Newton's method update equation *beginning* with the derivative, and with the desire to find a zero point of it.  Let us go about doing this."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "DIlS-sLQKpNf"
   },
   "source": [
    "So, suppose start from scratch and we do not know about Newton's method, we are simply looking for an iterative way to find a zero of our cost function derivative $g^{\\prime}(w) = 0$  - What could we do?  Finding zeros of an arbitrary function is not a trivial affair. As with our discussion of the first order condition - where we discussed just this issue - we would in general look to develop an iterative scheme for *approximating* zero points of an arbitrary function $g^{\\prime}$.  If we followed precisely the intuition that led us to gradient descent we would likewise conclude that while it is difficult to compute the zero of arbitrary function, it is trivial to compute where a line or hyperplane.  So why not repeatedly seek out the zero point(s) of the first order Taylor series approximation (a tangent line or hyperplane) to the function $g^{\\prime}$?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bRdd1O54KpNf"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 1. </span>  Illustrating the zero-finding algorithm concept"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "jRq6iWW_KpNg"
   },
   "source": [
    "Below we animate the iterative scheme for finding a zero of an arbitrary function $g^{\\prime}$ - here a sinusoid - based on repeatedly using the tangent line (our first order approximation) to a function and finding its zero.  As yo move the slider from left to right the scheme progresses with the point of tangency shown as a colored circle, with its corresponding input shown as an 'x' symbol.  The tangent point / input point along with the tangent line are all colored green - when the method begins - and transition to red as the method halts.  The input where the tangent line crosses the input axis is marked with a white 'x' symbol at each step, and the corresponding function evaluation (the point at which the next tangent line will be drawn) is shown as a white circle.  Moving the slider from left to right progresses the algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "93eWL8nXKpNg",
    "outputId": "8583d31b-09a6-4812-b999-f7a4ed6120dc"
   },
   "outputs": [
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 400x400 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what function should we play with?  Defined in the next line, along with our fixed point where we show tangency.\n",
    "g = lambda w: np.sin((w - 3))\n",
    "\n",
    "# create an instance of the visualizer with this function\n",
    "st = section_4_7_helpers.newton_secant_zero_finder_visualizer(g = g)\n",
    "\n",
    "# run the visualizer for our chosen input function and initial point\n",
    "st.draw_it_newton(savepath = video_path_1,w_init = 1,fps=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 421
    },
    "id": "YWeT63UyK2_a",
    "outputId": "acd03a95-bff0-41cb-8716-d1a76d000bf6"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=400 controls><source 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\"></video>"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_video(video_path_1, width=400)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "W7BMrnhAKpNh"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qrqEnOrFKpNi"
   },
   "source": [
    "To write out the first step of this scheme, remember first and foremost that we are thinking of this as an iterative method applied to the derivative function $g^{\\prime}(w)$ - this is the function we want to find zero points of i.e., inputs where $g^{\\prime}(w) = 0$.  This means - beginning at a point $w^0$ - that our linear approximation to the derivative function naturally involves the *second derivative* of the function $g$.  We can write the first order Taylor series linear approximation to the derivative function at $w^0$ as\n",
    "\n",
    "\\begin{equation}\n",
    "h\\left(w^0\\right) = g^{\\prime}\\left(w^0\\right) + g^{\\prime \\prime}\\left(w^0\\right)\\left(w - w^0\\right).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vXrWACSTKpNi"
   },
   "source": [
    "Here the second derivative $g^{\\prime \\prime}\\left(w^0 \\right)$ is the slope of the tangent line to $g^{\\prime}$ at the point $w^0$.  We can easily compute where this line crosses the input axis by setting the equation above to zero\n",
    "\n",
    "\\begin{equation}\n",
    "g^{\\prime}\\left(w^0\\right) + g^{\\prime \\prime}\\left(w^0\\right)\\left(w - w^0\\right) = 0\n",
    "\\end{equation}\n",
    "\n",
    "and solving for $w$.  Doing this, and calling the solution $w^1$, we have \n",
    "\n",
    "\\begin{equation}\n",
    "w^1 = w^0 - \\frac{g^{\\prime}\\left(w^0\\right)}{g^{\\prime \\prime}\\left(w^0\\right) }.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "GRg83xYiKpNi"
   },
   "source": [
    "If we then repeat this procedure - finding where the tangent line at $w^1$ crosses the input axis and solving for the next update etc., - then the $k^{th}$ update step then look like\n",
    "\n",
    "\\begin{equation}\n",
    "w^k = w^{k-1} - \\frac{g^{\\prime}\\left(w^{k-1}\\right)}{g^{\\prime \\prime}\\left(w^{k-1}\\right) }.\n",
    "\\end{equation}\n",
    "\n",
    "Notice - these are Newton steps!  So - in other words - we have re-derived Newton's method as a zero-finding algorithm for directly solving the first order optimality condition for single input functions.\n",
    "\n",
    "Precisely the same reasoning as we followed above for multi-input functions leads to the multi-input Newton's step as well.  So - indeed - we can view Newton's method simultaneously as\n",
    "\n",
    "- a method for determining a stationary point (preferably a minimum) of a cost function $g(\\mathbf{w})$\n",
    "\n",
    "\n",
    "- a method for finding a zero of the derivative function, i.e., where  $\\nabla g(\\mathbf{w}) = \\mathbf{0}_{N\\times 1}$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Z2paFhjEKpNi"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 2. </span>  Thinking of Newton's method in two ways simultaneously"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "du2juNznKpNj"
   },
   "source": [
    "Below we show an animation that simultaneously draws Newton's method from a) the perspective of minimizing a function (left panel) and b) finding the zero of its derivative(s) (right panel).  In particular we use the following function\n",
    "\n",
    "\\begin{equation}\n",
    "g(w) = \\frac{1}{50}\\left(w^4 + w^2 + 10w\\right).\n",
    "\\end{equation}\n",
    "\n",
    "As you move the slider from left to right Newton's method proceeds in both panels, with the final step shown when the slider is moved all the way to the right.  At each step in the algorithm the input and point of tangency are drawn as a white circle and 'x' symbol respectively, while the next step input / tangency are colored from green to red as the method proceeds.  The tangent quadratic / line is also drawn in each panel, and are colored from green to red as the method proceeds as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "3lRglTdvKpNj",
    "outputId": "cc051ab5-a08a-4e65-cf6a-0fe579d9360c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what function should we play with?  Defined in the next line.\n",
    "g = lambda w: 1/float(50)*(w**4 + w**2 + 10*w)   # try other functions too!  Like g = lambda w: np.cos(2*w) , g = lambda w: np.sin(5*w) + 0.1*w**2, g = lambda w: np.cos(5*w)*np.sin(w)\n",
    "\n",
    "# create an instance of the visualizer with this function\n",
    "minimize_zerofind = section_4_7_helpers.minimize_zero_find_simultaneous_visualizer(g = g)\n",
    "\n",
    "# run the visualizer for our chosen input function, initial point, and step length alpha\n",
    "minimize_zerofind.draw_it_newtons(w_init = 2.75,max_its = 20,savepath=video_path_2,fps=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "id": "ljxl1fhWK9bt",
    "outputId": "aa7990dd-4a99-416a-c4bc-183648f98442"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=800 controls><source 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_video(video_path_2, width=800)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V0cjeQUCKpNj"
   },
   "source": [
    "## Approximating the second derivative and the secant method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LckD_8_-KpNk"
   },
   "source": [
    "Remember (as discussed in Chapter 3) that the derivative of a single input function defines the slope of the tangent line to a function at a point.  Moreover the derivative/slope of a tangent line can be roughly approximated as the slope of a nearby *secant line*, that is a line that passes through the same point as well as another point nearby on the function (see Section 3.2).\n",
    "\n",
    "Using this fact in our current scenario of Newton's method as a zero-finding algorithm, we can then say that the slope of the tangent line to our derivative function $g^{\\prime}(w)$ - this slope being the second derivative itself $g^{\\prime \\prime}(w)$ - can itself be approximated by the slope of a nearby secant line as\n",
    "\n",
    "\\begin{equation}\n",
    "g^{\\prime\\prime}(w) \\approx \\frac{g^{\\prime}(w^{\\,}) - g^{\\prime}(v^{\\,})}{w^{\\,} - v^{\\,}}\n",
    "\\end{equation}\n",
    "\n",
    "if $v$ is taken close enough to the evaluation point $w$.  Using this rule somewhat loosely if we then go back to our Newton step and swap out the second derivative evaluation with this secant approximation we have a generic step that looks like\n",
    "\n",
    "\\begin{equation}\n",
    "w^k = w^{k-1} - \\frac{g^{\\prime}\\left(w^{k-1}\\right)}{ \\frac{g^{\\prime}(w^{k-1}) - g^{\\prime}(w^{k-2})}{w^{k-1} - w^{k-2}} }.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HnXNfQeaKpNk"
   },
   "source": [
    "We can write this less cumbersomely as\n",
    "\n",
    "\\begin{equation}\n",
    "w^k = w^{k-1} - \\frac{g^{\\prime}\\left(w^{k-1}\\right)}{s^{k-1}}\n",
    "\\end{equation}\n",
    "\n",
    "where $s^{k-1}$ has been used to replace the second derivative, and is defined as\n",
    "\n",
    "\\begin{equation}\n",
    "s^{k-1} = \\frac{g^{\\prime}(w^{k-1}) - g^{\\prime}(w^{k-2})}{w^{k-1} - w^{k-2}}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Hj9d3MSQKpNk"
   },
   "source": [
    " This approach - called the *Secant method* since it employs a secant instead of a tangent line - can still determine zeros of a derivative function $g^{\\prime}(w)$ / stationary points of the cost $g(w)$, but without the explicit need for the second derivative.  This fact - while fairly inconsequential for a $N = 1$ dimensional input function - gains significantly more value when the *Secant method* idea is generalized to multi-input functions (since it is the very size of the Hessian that prohibits Newton's method's use for function's with larger values of $N$)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "x49bYeVYKpNk"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 3. </span>  The Secant method from two perspectives"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nH6wrFTqKpNk"
   },
   "source": [
    "Below we show an animation that simultaneously draws the Secant method from a) the perspective of minimizing a function (left panel) and b) finding the zero of its derivative(s) (right panel).  In particular we use the following function\n",
    "\n",
    "\\begin{equation}\n",
    "g(w) = \\frac{1}{50}\\left(w^4 + w^2 + 10w\\right).\n",
    "\\end{equation}\n",
    "\n",
    "As you move the slider from left to right Newton's method proceeds in both panels, with the final step shown when the slider is moved all the way to the right.  At each step in the algorithm the input and point of tangency are drawn as a white circle and 'x' symbol respectively, while the next step input / tangency are colored from green to red as the method proceeds.  The tangent quadratic / line is also drawn in each panel, and are colored from green to red as the method proceeds as well."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 297
    },
    "id": "dbMAboFeKpNk",
    "outputId": "81fb92a3-d2b7-4daa-9471-ab8a7d8edd2c"
   },
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1200x400 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# what function should we play with?  Defined in the next line.\n",
    "g = lambda w: 1/float(50)*(w**4 + w**2 + 10*w)   # try other functions too!  Like g = lambda w: np.cos(2*w) , g = lambda w: np.sin(5*w) + 0.1*w**2, g = lambda w: np.cos(5*w)*np.sin(w)\n",
    "\n",
    "# create an instance of the visualizer with this function\n",
    "minimize_zerofind = section_4_7_helpers.minimize_zero_find_simultaneous_visualizer(g = g)\n",
    "\n",
    "# run the visualizer for our chosen input function, initial point, and step length alpha\n",
    "minimize_zerofind.draw_it_secant(savepath=video_path_3,w_init = 2.75,max_its = 20,fps=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 288
    },
    "id": "bQFSA6Z4LAPu",
    "outputId": "ad042b96-fc10-473c-eb0d-88d1d7066120"
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<video width=800 controls><source 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      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "show_video(video_path_3, width=800)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9frvSutFKpNl"
   },
   "source": [
    "## The general $N$ dimensional input Secant method "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "3BuntR1UKpNl"
   },
   "source": [
    "Everything we have discussed for the generic single input $N= 1$ dimensional case tracks to the higher dimensional instance as well, with one important difference.  Looking back at the Subsection above we replaced the second derivative with the slope of the corresponding secant line $s^{k-1} = \\frac{g^{\\prime}(w^{k-1}) - g^{\\prime}(w^{k-2})}{w^{k-1} - w^{k-2}}$ as\n",
    "\n",
    "\\begin{equation}\n",
    "g^{\\prime \\prime}(w^{k-1}) \\longleftarrow s^{k-1}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wfijqv4dKpNl"
   },
   "source": [
    "What is this analogous replacement when $N > 1$?   Abusing notation for a moment, we could express it as (this is incorrect mathematically speaking, but the algebra mirrors the one dimensional case) by literally just upgrading each piece of notation on the right hand side of the equality above to its vector analog giving \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{S}^{k-1} = \\frac{\\nabla g\\left(\\mathbf{w}^{k-1}\\right) - \\nabla g\\left(\\mathbf{w}^{k-2}\\right)}{\\mathbf{w}^{k-1} - \\mathbf{w}^{k-2}}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "7o-xdrkFKpNl"
   },
   "source": [
    "In this case, since we are replacing the Hessian the variable $\\mathbf{S}^{k-1}$ must also be an $N\\times N$ matrix.  However we cannot - strictly speaking - express the right hand side of the equality above, since this would mean we are (algebraically) dividing $N$ an length vector (the numerator) by an $N$ length vector (the denominator).   The proper $N$ dimensional analog of the $N=1$ dimensional replacement is in fact a solution to the system\n",
    "\n",
    "\\begin{equation}\n",
    " \\mathbf{S}^{k-1}\\left(\\mathbf{w}^{k-1} - \\mathbf{w}^{k-2}\\right)  =   \\nabla g\\left(\\mathbf{w}^{k-1}\\right) - \\nabla g\\left(\\mathbf{w}^{k-2}\\right).\n",
    "\\end{equation}\n",
    "\n",
    "Likewise - inverting $\\mathbf{S}^{k-1}$ - we could express this statement as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{w}^{k-1} - \\mathbf{w}^{k-2} =   \\left(\\mathbf{S}^{k-1}\\right)^{-1}\\left(\\nabla g\\left(\\mathbf{w}^{k-1}\\right) - \\nabla g\\left(\\mathbf{w}^{k-2}\\right)\\right)\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pjn9mMBUKpNl"
   },
   "source": [
    "In either case notice that the variable we must solve for is here is the matrix $\\mathbf{S}^{k-1}$ (or $\\left(\\mathbf{S}^{k-1}\\right)^{-1}$) itself.  This is often called the *secant condition*, since it is indeed the $N$ dimensional analog of the slope of the one dimensional secant line defined by the second derivative.  So - if this system can be solved - we make the analog replacement of $g^{\\prime \\prime}(w^{k-1}) \\longleftarrow s^{k-1} $ to the $N$ dimensional case, replacing the the full Hessian matrix \n",
    "\n",
    "\\begin{equation}\n",
    "\\nabla^2 g\\left(\\mathbf{w}^{k-1}\\right) \\longleftarrow \\mathbf{S}^{k-1}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JoSwNsOiKpNl"
   },
   "source": [
    "However unlike the $N = 1$ dimensional case - where each update has a closed form update - the system we must solve in equation (16) for our secant replacement $\\mathbf{S}^{k-1}$ will always have has infinitely many solutions.  There are only $N$ equations, but $N^2$ entries to solve for in the matrix $\\mathbf{S}^{k-1}$.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "hxHDqOAGKpNl"
   },
   "source": [
    "## Quasi-Newton methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "oOkeYff6KpNl"
   },
   "source": [
    "As discussed in Section 7.3, as a *local optimization* step $\\mathbf{w}^k = \\mathbf{w}^{k-1} + \\alpha \\mathbf{d}^{k}$ the standard Newton method update \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{w}^{k} = \\mathbf{w}^{k-1} - \\left(\\nabla^2 g(\\mathbf{w}^{k-1})\\right)^{-1}\\nabla g(\\mathbf{w}^{k-1}).\n",
    "\\end{equation}\n",
    "\n",
    "is a local optimization step with descent direction given by \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{d}^{k} = - \\left(\\nabla^2 g(\\mathbf{w}^{k-1})\\right)^{-1}\\nabla g(\\mathbf{w}^{k-1}).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "R_hmnuBRKpNm"
   },
   "source": [
    "*Quasi-Newton methods* is the jargon phrase for any descent step of the form above where we replace the true Hessian in this descent direction with an inverse secant matrix $\\mathbf{S}^{k-1}$ as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{d}^{k} = - \\left(\\mathbf{S}^{k-1}\\right)^{-1}\\nabla g(\\mathbf{w}^{k-1}).\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mlRR00-1KpNo"
   },
   "source": [
    "In replacing the true Hessian with a secant approximation we no longer need compute second derivatives or - as we will see - store an entire $N\\times N$ matrix to construct a Newton-like descent direction.  In doing so however Quasi-Newton methods lose some of their minimization speed (being at best *superlinear* instead of *quadratic* in terms of their convergence properties)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "4cdnq3-6KpNo"
   },
   "source": [
    "But with infinitely many possible secant matrices $\\mathbf{S}^{k-1}$ to choose from, how to we choose a 'good' one?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mdzUggwDKpNo"
   },
   "source": [
    "Because we want $\\mathbf{S}^{k-1}$ / $\\left(\\mathbf{S}^{k-1}\\right)^{-1}$ to be as similar as possible to its analagous Hessian we can introduce a number of reasonable *constraints* to limit the range of solutions to this system.  Here are a few obvious characteristics we want $\\mathbf{S}^{k-1}$ to have (in order for it to mimic the Hessian).  This same list also applies to the inverse secant matrix $\\left(\\mathbf{S}^{k-1}\\right)^{-1}$ as well.\n",
    "\n",
    "1) **$\\mathbf{S}^{k-1}$ should be a solution to the secant condition**\n",
    "\n",
    "\n",
    "2) **$\\mathbf{S}^{k-1}$ should be symmetric:** the Hessian $\\nabla^{2}g\\left(\\mathbf{w}^{k-1}\\right)$ is always symmetric, so $\\mathbf{S}^{k-1}$ should be too\n",
    "\n",
    "\n",
    "\n",
    "3) **$\\mathbf{S}^{k}$ should not differ substantially from $\\mathbf{S}^{k-1}$:** the Hessian $\\nabla^{2}g\\left(\\mathbf{w}\\right)$ is continuous, so\n",
    "our approximations $\\mathbf{S}^{k}$ and $\\mathbf{S}^{k-1}$ should\n",
    "not differ too wildly"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "snWBQqOHKpNo"
   },
   "source": [
    "With these conditions in mind, there are still a number of possible ways to construct $\\mathbf{S}^{k-1}$ or $\\left(\\mathbf{S}^{k-1}\\right)^{-1}$, which we explore by example below.  These constructions are *recursive* in nature, so that we can assure that condition $3)$ above holds, and take the general form \n",
    "\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{S}^k\\right)^{-1} = \\left(\\mathbf{S}^{k-1}\\right)^{-1} + \\mathbf{D}^{k-1}\n",
    "\\end{equation}\n",
    "\n",
    "where the $N\\times N$ matrix $\\mathbf{D}^{k-1}$ is designed to be symmetric (so that condition $2)$ holds) and of a particular rank (so that the form of $\\mathbf{D}^{k-1}$ can be computed in closed form / effectively in practice).  The same sort of recursion can be constructed for $\\mathbf{S}^k$ as well, as we will see below."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "LeYQvNO8KpNo"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "ooMJkn2BKpNp"
   },
   "source": [
    "Taken together and translated into the language of math these conditions provoke a *constrained optimization problem* for recovering a solution matrix $\\mathbf{S}^k$ with these properties.  This constrained problem takes the form\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}{cc}\n",
    "\\underset{\\mathbf{S}}{\\text{minimize}} & \\left\\Vert \\mathbf{S}^{\\,}-\\mathbf{S}^{k-1}\\right\\Vert _{F}^{2}\\\\\n",
    "\\text{subject to} & \\mathbf{S}\\mathbf{a}^{k}=\\mathbf{b}^{k}\\\\\n",
    " & \\mathbf{S} \\,\\,\\, \\text{symmetric}\n",
    "\\end{array}\n",
    "\\end{equation}\n",
    "\n",
    "where as before $\\mathbf{a}^k = \\mathbf{w}^{k-1} - \\mathbf{w}^{k-2}$ and $\\mathbf{b}^k = \\nabla g(\\mathbf{w}^{k-1}) - \\nabla g(\\mathbf{w}^{k-2})$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "l65T1qKqKpNp"
   },
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "UAYLZpAzKpNp"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 4. </span>  Rank 1 update formula"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kWFetFCZKpNp"
   },
   "source": [
    "In this example we describe one of the simplest recursive formula for $\\mathbf{S}^{k}$ or its inverse based on a *rank one* update.  To see how this formula is derived let use the inverse.  Taking our secant update employing the inverse matrix $\\left(\\mathbf{S}^{k}\\right)^{-1}$\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{w}^{k-1} - \\mathbf{w}^{k-2} =   \\left(\\mathbf{S}^{k}\\right)^{-1}\\left(\\nabla g\\left(\\mathbf{w}^{k-1}\\right) - \\nabla g\\left(\\mathbf{w}^{k-2}\\right)\\right)\n",
    "\\end{equation}\n",
    "\n",
    "lets first simplify it using some temporary notation by letting $\\mathbf{a}^k = \\mathbf{w}^{k-1} - \\mathbf{w}^{k-2}$, $\\mathbf{F}^{k} = \\left(\\mathbf{S}^{k}\\right)^{-1}$, and $\\mathbf{c}^k = \\nabla g\\left(\\mathbf{w}^{k-1}\\right) - \\nabla g\\left(\\mathbf{w}^{k-2}\\right) $.  In this notation we can write the above equivalently as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{a}^k  =   \\mathbf{F}^k\\mathbf{b}^k.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kL8o-X66KpNp"
   },
   "source": [
    "Since we want $\\mathbf{F}^k$ to not differ too much from its predecessor $\\mathbf{F}^{k-1}$ and we want it to be symmetric, a natural first attempt at constructing the matrix is to suppose that these two matrices differ only by a *rank one outer-product matrix* as\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{F}^{k} = \\mathbf{F}^{k-1} + \\mathbf{v}^{,}\\mathbf{v}^T.\n",
    "\\end{equation}\n",
    "\n",
    "This formula satisifes desire $1)$ above insofar as two matrices $\\mathbf{F}^{k}$ and $\\mathbf{F}^{k-1}$ can be similar if they differ by a rank one matrix.  Notice that it also satisfies desire $3)$ since the $N\\times N$ matrix $\\mathbf{v}^{,}\\mathbf{v}^T$, being a rank one outer product matrix, is *always* symmetric.  Thus if we *initialize* the very first $\\mathbf{F}^0$ to a symmetric matrix (most commonly the identity) this update will retain our desired symmetry property (since the sum of two symmetric matrices is always symmetric).  Moreover, if the initialization $\\mathbf{F}^0$ is *positive definite* (as the identity matrix is) then this property is inhereited by all matrices $\\mathbf{F}^k$ via this formula so long as $\\mathbf{v}$ is computable (hence condition $4)$ will be satisfied as well)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qTihdSycKpNq"
   },
   "source": [
    "But we also want this update to satisfy desire $2)$ above (the secant condition).  By *assuming* the update above does indeed satisfy the secant condition we can then work *backwards* from it to determine the proper value for our $N\\times1$ vector $\\mathbf{v}$.\n",
    "\n",
    "To being we first plug in our assumed rank one update structure for $\\mathbf{F}^k$ into the secant condition above, which gives\n",
    "\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{F}^{k-1} + \\mathbf{v}^{,}\\mathbf{v}^T\\right)\\mathbf{b}^k = \\mathbf{F}^{k-1}\\mathbf{b}^k  +\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k = \\mathbf{a}^k  \n",
    "\\end{equation}\n",
    "\n",
    "or rearranging equivalently \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k  = \\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k.\n",
    "\\end{equation}\n",
    "\n",
    "What value does $\\mathbf{v}$ need to take on in order for "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "uh4sgmPfKpNq"
   },
   "source": [
    "To see let us first *left* multiply the entire formula above by $\\mathbf{b}^k$ gives\n",
    "\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{b}^k\\right)^T\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k = \\left(\\mathbf{v}^{T}\\mathbf{b}^k\\right)^2 = \\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k  \n",
    "\\end{equation}\n",
    "\n",
    "or taking the square root of both sides\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{v}^{T}\\mathbf{b}^k = \\left(\\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^{\\frac{1}{2}}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5fB-jMDqKpNq"
   },
   "source": [
    "Now because note that $\\mathbf{v}^{T}\\mathbf{b}^k$ is a *constant* we can divide if from both sides of equation (24) above, giving\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{v} = \\frac{ \\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k}{ \\left(\\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^{\\frac{1}{2}}.}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Nv9FxwNLKpNq"
   },
   "source": [
    "This formula gives closed form expression for $\\mathbf{v}$, and therefore the rank one update formula in equation (22).  The corresponding rank one formula with this value for $\\mathbf{v}$ plugged in is then\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{F}^{k} = \\mathbf{F}^{k-1} +  \\frac{\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right)\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^T}{ \\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "nMtA5jOpKpNq"
   },
   "source": [
    "This update is for the inverse matrix $\\mathbf{F}^{k} = \\left(\\mathbf{S}^{k}\\right)^{-1}$ - which we need in order compute our secant-based Quasi-Newton descent direction.  However note that an entirely similar recursive expression for $\\mathbf{S}^k$ can be formulated by starting with the same assumption (a recursion based on a rank one difference between $\\mathbf{S}^k$ and its predecessor) and employing the corresponding secant condition as was done here.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "iQAysubRKpNq"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 4. </span>  Rank two update formulae (DFP)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "FhOvr2u3KpNq"
   },
   "source": [
    "The next logical desired update step after a rank one update (seen in the previous example) is a *rank two* update formula.  Using the same notation as in the prior example, we want to determine proper $N\\times 1$ vectors $\\mathbf{u}$ and $\\mathbf{v}$ so that\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{F}^{k} = \\mathbf{F}^{k-1} + \\mathbf{u}^{,}\\mathbf{u}^T + \\mathbf{v}^{,}\\mathbf{v}^T.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "04lgxxG1KpNq"
   },
   "source": [
    "By allowing for a rank two difference between the subsequent matrices - as opposed to a rank one difference - we encode an additional level of complexity into our approximation to subsequent inverse Hessian evaluations.  This formula update satisfies desire 1), insofar as two matrices $\\mathbf{F}^{k}$ and $\\mathbf{F}^{k-1}$ can be similar if they differ by a rank two matrix.  It also satisfies desire $3)$ since the $N\\times N$ matrix  $\\mathbf{u}^{,}\\mathbf{u}^T + \\mathbf{v}^{,}\\mathbf{v}^T$, being a rank two outer product matrix, is *always* symmetric.  Thus if we *initialize* the very first $\\mathbf{F}^1$ to a symmetric matrix (most commonly the identity) this update will retain our desired symmetry property (since the sum of two symmetric matrices is always symmetric).   Moreover, if the initialization $\\mathbf{F}^0$ is *positive definite* (as the identity matrix is) then this property is inhereited by all matrices $\\mathbf{F}^k$ via this formula so long as $\\mathbf{v}$ is computable (hence condition $4)$ will be satisfied as well)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "H6qdxTsXKpNq"
   },
   "source": [
    "In order to determine the proper values for $\\mathbf{u}$ and $\\mathbf{v}$ we assume - as we did in the prior example - that this update satisfies the secant condition (desire 2)).\n",
    "\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{F}^{k-1} + \\mathbf{u}^{,}\\mathbf{u}^T + \\mathbf{v}^{,}\\mathbf{v}^T\\right)\\mathbf{b}^k = \\mathbf{F}^{k-1}\\mathbf{b}^k  + \\mathbf{u}^{,}\\mathbf{u}^T\\mathbf{b}^k  +\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k = \\mathbf{a}^k.\n",
    "\\end{equation}\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true,
    "id": "2jXMxmJaKpNr"
   },
   "source": [
    "or rearranging equivalently \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{u}^{,}\\mathbf{u}^T\\mathbf{b}^k  + \\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k  = \\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Gv5vF_Z8KpNr"
   },
   "source": [
    "What values can $\\mathbf{u}$ and $\\mathbf{v}$ take on in order for the equality above to hold?  Here we have a single equation, but *two* unknown values $\\mathbf{u}$ and $\\mathbf{v}$ - so there are infinitely many choices for proper $\\mathbf{u}$ and $\\mathbf{v}$.  A very simple yet very common way of determiing a single set of values for $\\mathbf{u}$ and $\\mathbf{v}$ is to suppose: the first term on the left hand side above / right hand side above equals the corresponding term on the right hand side.  That is we make the simple assumption that the following two formula hold (which implies that the secant formula above holds as well)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vSai59ZlKpNr"
   },
   "source": [
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\mathbf{u}^{,}\\mathbf{u}^T\\mathbf{b}^k = \\mathbf{a}^k \\\\\n",
    "\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k = - \\mathbf{F}^{k-1}\\mathbf{b}^k.\n",
    "\\end{array}\n",
    "\\end{equation}\n",
    "\n",
    "This added assumption allows us to solve for a valid pair of $\\mathbf{u}$ / $\\mathbf{v}$ in a way that closely mirrors the solution method from the previous example.  That is, first we will *left multiply* each of these formula by $\\mathbf{b}^k$.  Doing this to each equation above we have\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\left(\\mathbf{b}^k\\right)^T\\mathbf{u}^{,}\\mathbf{u}^T\\mathbf{b}^k = \\left(\\mathbf{u}^{T}\\mathbf{b}^k\\right)^2  =  \\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k \\\\\n",
    "\\left(\\mathbf{b}^k\\right)^T\\mathbf{v}^{,}\\mathbf{v}^T\\mathbf{b}^k = \\left(\\mathbf{v}^{T}\\mathbf{b}^k\\right)^2  =  - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k.\n",
    "\\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "OPfu6DZsKpNr"
   },
   "source": [
    "Taking the square root of both sides in both equations above we then have the set of equations\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\mathbf{u}^{T}\\mathbf{b}^k  =  \\left(\\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k\\right)^{\\frac{1}{2}} \\\\\n",
    "\\mathbf{v}^{T}\\mathbf{b}^k  =  \\left(- \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^{\\frac{1}{2}}.\n",
    "\\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "436-1uMHKpNr"
   },
   "source": [
    "We can now divide off the top / bottom constants from the top / bottom formulae in equation (32) respectively, giving  \n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\mathbf{u} = \\frac{\\mathbf{a}^k}{\\left(\\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k\\right)^{\\small{\\frac{1}{2}}} } \\\\\n",
    "\\mathbf{v}= \\frac{-\\mathbf{F}^{k-1}\\mathbf{b}^k}{\\left(- \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^{\\small{\\frac{1}{2}}}}.\n",
    "\\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "a0T2R5GjKpNr"
   },
   "source": [
    "This formula gives closed form expressions for $\\mathbf{u}$ and $\\mathbf{v}$ (and is often called the Davidon-Fletcher-Powell (DFP) Method based on the authors who first put forth this solution), given that we make a simple but stronger assumption than the secand condition alone, that when plugged into the rank two update formula in equation (29) gives\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{F}^{k} = \\mathbf{F}^{k-1} + \\frac{\\mathbf{a}^k \n",
    "\\left(\\mathbf{a}^k\\right)^T}{\\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k } -   \\frac{\\left(\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)\\left(\\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^T}{\\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k}.\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "wWJ0n_AwKpNs"
   },
   "source": [
    "#### <span style=\"color:#a50e3e;\">Example 5. </span>  Rank two update formulae (BFGS)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JUYi3vb8KpNs"
   },
   "source": [
    "While the update in the previous example was for the inverse matrix $\\mathbf{F}^{k} = \\left(\\mathbf{S}^{k}\\right)^{-1}$ an entirely similar recursive expression for $\\mathbf{S}^k$ can be formulated by starting with the same assumption (a recursion based on a rank two difference between $\\mathbf{S}^k$ and its predecessor) and employing the corresponding secant condition as was done here.  Doing this - where $\\mathbf{F}^{k} = \\mathbf{S}^{k}$ - we can write the analagous update for $\\mathbf{S}^k$ as \n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{S}^{k} = \\mathbf{S}^{k-1} + \\frac{\\mathbf{b}^k \n",
    "\\left(\\mathbf{b}^k\\right)^T}{\\left(\\mathbf{a}^k\\right)^T\\mathbf{b}^k } -   \\frac{\\left(\\mathbf{S}^{k-1}\\mathbf{a}^k\\right)\\left(\\mathbf{S}^{k-1}\\mathbf{a}^k\\right)^T}{\\left(\\mathbf{a}^k\\right)^T\\mathbf{S}^{k-1}\\mathbf{a}^k}.\n",
    "\\end{equation}\n",
    "\n",
    "This formula is often referred to as the Broyden–Fletcher–Goldfarb–Shanno (BFGS) update, named after its original authors."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "qG47VJqgKpNs"
   },
   "source": [
    "While this is a valid formula for $\\mathbf{S}^k$, in order to compute a secant-based Quasi-Newton descent step we would like to use its inverse $\\left(\\mathbf{S}^{k}\\right)^{-1}$.  While we have already computed an analagous rank two formula in the prior example, technically speaking we can also get a rank two formula by *inverting*  the one we have for $\\mathbf{S}^k$ above.  Doing this gives a different formula for $\\mathbf{F}^{k} = \\left(\\mathbf{S}^{k}\\right)^{-1}$\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\mathbf{F}^{k} = \\left(\\mathbf{S}^{k-1} + \\frac{\\mathbf{b}^k \n",
    "\\left(\\mathbf{b}^k\\right)^T}{\\left(\\mathbf{a}^k\\right)^T\\mathbf{b}^k } -   \\frac{\\left(\\mathbf{S}^{k-1}\\mathbf{a}^k\\right)\\left(\\mathbf{S}^{k-1}\\mathbf{a}^k\\right)^T}{\\left(\\mathbf{a}^k\\right)^T\\mathbf{S}^{k-1}\\mathbf{a}^k} \\right)^{-1}  \\\\\n",
    "= \\mathbf{F}^{k-1} + \\frac{\\left( \\left(\\mathbf{a}^k\\right)^T\\mathbf{b}^k +  \n",
    "\\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k\\right) \\mathbf{a}^k\\left(\\mathbf{a}^k\\right)^T}{\\left(\\left(\\mathbf{a}^k\\right)^T\\mathbf{b}^k \\right)^2} -   \\frac{\\mathbf{F}^{k-1}\\mathbf{b}^k\\left(\\mathbf{a}^{k}\\right)^T + \\mathbf{a}^{k}\\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1} }{\\left(\\mathbf{a}^k\\right)^T\\mathbf{b}^k}\n",
    "\\end{array}\n",
    "\\end{equation}\n",
    "\n",
    "where the formula on the right hand side follows from the Sherman–Morrison identity."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "Mlml_pKAKpNs"
   },
   "source": [
    "This BFGS formula for the inverse secant tends to work better in practice than the DFP version given in the prior example, and so is more popularly used in practice."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "V5WYcEV0KpNs"
   },
   "source": [
    "## Low memory Quasi-Newton methods"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "PN13QumjKpNs"
   },
   "source": [
    "The general inverse secant update formula we saw in the examples above\n",
    "\n",
    "\\begin{equation}\n",
    "\\left(\\mathbf{S}^k\\right)^{-1} = \\left(\\mathbf{S}^{k-1}\\right)^{-1} + \\mathbf{D}^{k-1}\n",
    "\\end{equation}\n",
    "\n",
    "where the $N\\times N$ matrix $\\mathbf{D}^{k-1}$ is designed to be symmetric and of a particular rank, provides us with a way of constructing $\\left(\\mathbf{S}^k\\right)^{-1}$ from its predecessor so that it behaves like a true Hessian matrix.  Using any of these update formulae the *descent direction* for a Quasi-Newton step (as noted previously) is\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{d}^{k} = - \\left(\\mathbf{S}^{k-1}\\right)^{-1}\\nabla g(\\mathbf{w}^{k-1})\n",
    "\\end{equation}\n",
    "\n",
    "where $\\mathbf{S}^{k-1}$ is our approximation to the true Hessian matrix.\n",
    "\n",
    "However as written our secant matrix update rules *still involve explicit forms of an $N\\times N$ matrix*, i.e., the secant $\\mathbf{S}^{k}$ or its inverse $\\left(\\mathbf{S}^k\\right)^{-1}$.  However, if you recall (see Section 7.4), that it was precisely the presence of the $N\\times N$ Hessian matrix (with its $N^2$ values) that drove us to examine Quasi-Newton methods to begin with.  So it appears that we have not avoided the serious scaling issues associated with employing an $N\\times N$ matrix (originally a Hessian matrix, now a secant matrix)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "vAblE0w1KpNs"
   },
   "source": [
    "We can in fact avoid constructing the secant matrix *explicitly* by focusing on *how we use it* - which is via matrix-vector multiplication in computing our descent direction $\\mathbf{d}^{k} = - \\left(\\mathbf{S}^{k-1}\\right)^{-1}\\nabla g(\\mathbf{w}^{k-1})$ - and by computing this direction intelligently.  In other words, when implementing we do not need to *explicitly* store $\\left(\\mathbf{S}^{k-1}\\right)^{-1}$ but we do need to explicitly compute the matrix-vector products of the form $\\left(\\mathbf{S}^{k-1}\\right)^{-1} \\mathbf{z}$ where $\\mathbf{z}$ is an arbitrary $N\\times N$ vector.   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "9NQX6_haKpNt"
   },
   "source": [
    "If we take one of the formulae for our inverse secant matrix derived above, we can see how to explicitly compute such a product while avoiding the explicit construction of any $N\\times N$ inverse secant matrix with the exception of our initialization $\\left(\\mathbf{S}^{0}\\right)^{-1}$.   For example, if we take our *rank one update formula* for the inverse secant detailed in Example 4 above - using the notation introduced in there - and compute $\\left(\\mathbf{S}^{k}\\right)^{-1} \\mathbf{z}=\\mathbf{F}^{k} \\mathbf{z}$ we have\n",
    "\n",
    "\\begin{equation}\n",
    "\\begin{array}\n",
    "\\\n",
    "\\mathbf{F}^{k} \\mathbf{z} =  \\left(\\mathbf{F}^{k-1} +  \\frac{\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right)\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^T}{ \\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k}\\right)\\mathbf{z}  \\\\\n",
    "= \\mathbf{F}^{k-1}\\mathbf{z} +  \\frac{\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right)^T\\mathbf{z}}{ \\left(\\mathbf{b}^k\\right)^T\\mathbf{a}^k - \\left(\\mathbf{b}^k\\right)^T\\mathbf{F}^{k-1}\\mathbf{b}^k}\\left(\\mathbf{a}^k - \\mathbf{F}^{k-1}\\mathbf{b}^k\\right).\n",
    "\\end{array}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "kXmD2kI0KpNt"
   },
   "source": [
    "If we think about the computation required above for $\\mathbf{F}^{k}\\mathbf{z}$ in terms of the *vectors* required, we need access too: $\\mathbf{a}^k$, $\\mathbf{b}^k$, $\\mathbf{z}$, $\\mathbf{F}^{k-1}\\mathbf{b}^k$, and $\\mathbf{F}^{k-1}\\mathbf{z}$.  In terms of just the matrix vector products (since it is the explicit storage of the matrices that we wish to avoid), we need only concern ourselves with the final two vectors and how we can compute them without explicitly storing $\\mathbf{F}^{k-1}$.  If we can do this then in computing the generic matrix-vector product $\\mathbf{F}^{k}\\mathbf{z}$ we can avoid explicit storage of the matrix $\\mathbf{F}^k$.  How can we do this?"
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    "Well, note that if we start with the first update $k=1$ and *initialize* $\\mathbf{F}^0 = \\mathbf{I}_{N\\times N}$ then we can compute the first descent direction simply as $\\mathbf{d}^1 = - \\mathbf{F}^0\\nabla g(\\mathbf{w}^{0}) = -\\nabla g(\\mathbf{w}^{0})$ (i.e., the gradient descent direction at $\\mathbf{w}^0$).\n",
    "Initializing with the identity also allows the first matrix-vector products to be computed trivially - that is $\\mathbf{F}^0\\mathbf{b}^1 = \\mathbf{b}^1$ and $\\mathbf{F}^0\\mathbf{z} = \\mathbf{z}$.  In other words, in addition to the first descent direction we can compute arbitrary products of the form $\\mathbf{F}^0\\mathbf{z}$.  This means that - via the rank one identity for forming $\\mathbf{F}^1$ above - that we can now form arbitrary matrix-vector products $\\mathbf{F}^1\\mathbf{z}$ involving our updated inverse secant $\\mathbf{F}^1$ *without the need to explicitly store $\\mathbf{F}^1$*.  In particular we can then compute the *second* descent direction $\\mathbf{d}^2 = - \\mathbf{F}^1\\nabla g(\\mathbf{w}^{1})$ without explicitly storing $\\mathbf{F}^1$.  Then if we can compute arbitrary matrix-vector products $\\mathbf{F}^1\\mathbf{z}$ without the need to store $\\mathbf{F}^1$ we can - using our identity to form $\\mathbf{F}^2$ - form the third descent step $\\mathbf{d}^3 = - \\mathbf{F}^2\\nabla g(\\mathbf{w}^{2})$ without the need to explicitly store $\\mathbf{F}^2$.  This pattern can be continued to the $k^{th}$ descent step where we can then compute $\\mathbf{d}^k = - \\mathbf{F}^{k-1}\\nabla g(\\mathbf{w}^{k-1})$ without the need to explicitly store $\\mathbf{F}^{k-1}$."
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    "We can almost entirely the same kind of argument can be made with any rank one or rank two Quasi-Newton update formula, meaning that any of the update formulae given in the preceeding examples can be implemented so that we never need store a secant or inverse secant matrix."
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